While our results demonstrate the existence of finite-amplitude arrowhead TWs over a very large range of the parameter space, a direct connection to either EIT or ET has yet to be established. In inertia-dominated EIT, instantaneous arrowhead-shaped flow structures resembling the stable upper branch states have been observed numerically [1]}.
While the region of nonlinear instability found here overlaps with these observations, further work is required to assess if there is a direct connection between the exact coherent states and EIT (e.g. through a sequence of successive bifurcations). At low-\(Re\) , our numerical experiments indicate that the upper branch TWs are linearly stable, and we have been unable to trigger ET. Our computations have been restricted to 2D flows, and so this does not rule out the existence of ET in three dimensions, or a direct route from the upper branch TWs to such a state. We hope to report results on this soon.
